Brocard's Problem: No Solution for n! Containing Prime^2, n>7?

  • Thread starter Thread starter secondprime
  • Start date Start date
secondprime
Messages
47
Reaction score
0
Brocard's problem asks to find integer values of n for which
n! + 1 =m^2 .
where n! is the factorial.Probably I got a proof that there is no solution if n! contains a prime with power exactly 2 & n>7...looking for error...anyone else with any result?
 
Last edited:
Physics news on Phys.org
and you did not post your proof because you run out of ink? or maybe your computer crashed.
 
I have enough ink but don't know how to write with ink on computer:smile: trying to find an error in my proof,so asking about any result related to the problem.
 
Using long integer arithmetic, I found (besides n= 4, 5, 7) no other solutions for all n < 100
 

Thread '##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?'

I asked online questions about Proposition 2.1.1: The answer I got is the following: I have some questions about the answer I got. When the person answering says: ##1.## Is the map ##\mathfrak{q}\mapsto \mathfrak{q} A _\mathfrak{p}## from ##A\setminus \mathfrak{p}\to A_\mathfrak{p}##? But I don't understand what the author meant for the rest of the sentence in mathematical notation: ##2.## In the next statement where the author says: How is ##A\to...
View full post »

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Similar threads

I Trouble understanding an online solution to an exercise in Dummit & Foote
Replies
12
Views
616
A Possible Proof for Brocard's Problem
Replies
3
Views
6K
I Understanding the ##ε## as used in limits of sequences
Replies
2
Views
2K
I I think I've hit upon a very easy proof of impossibility of quintic
Replies
2
Views
2K
Conjectures by Legendre and Brocard made stronger.
Replies
2
Views
3K
MHB Prove that CnXCm isomorphic to Cgcd(m,n)XClcm(m,n)
Replies
3
Views
2K
I Fourier Transformation on a Ring
Replies
11
Views
3K
The only prime of the form n^3-1 is 7?
Replies
2
Views
4K
For n>3, show that the integers n, n+2, n+4 cannot all be prime
Replies
27
Views
3K
B Probability that 2 distinct integers are divisible by the same number
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top